Problems on Linear Equation in Two Variable

Draw the graph of following ?

1. x + y = 2

2. x – y = 3

3. y = 2 x

4. 3 x + y = 4

Solution.

1. x + y = 2

Given : Linear Equations

x + y = 2 => y = 2 - x

When x = 0 then y = 2

When x = 1 then y = 1

When x = 2 then y = 0

When x = 3 then y = -1

So co-ordinates are (0,2), (1,1), (2,0), (3,-1)

2. x - y = 3

Given : Linear Equations

x - y = 3 => y = x – 3

When x = 0 then y = -3

When x = 1 then y = -2

When x = 2 then y = -1

When x = 3 then y = 0

So co-ordinates are (0,-3), (1,-2), (2,-1), (3,0)

3. y = 2 x

Given : Linear Equations

y = 2 x

When x = 0 then y = 0

When x = 1 then y = 2

When x = 2 then y = 4

When x = -1 then y = -2

So co-ordinates are (0,0), (1,-2), (2,4), (-1,-2)

maths ncert solutions

4. 3 x + y = 4

Given : Linear Equations

3 x + y = 4 => y = 4 – 3 x

When x = 0 then y = 4

When x = 1 then y = 1

When x = 2 then y = -2

When x = 3 then y = -5

So co-ordinates are (0,4), (1,1), (2,-2), (3,1)

5. Given the equation of two lines passing through (2,10). How many more such lines are there, and why ?

Solution.

Equation of two lines passing through (2,10)

It can be observed that point (2,10) satisfies the equation 5 x – y = 0 and x – y + 8 = 0

So 5 x – y = 0 and x – y + 8 = 0 are the two lines passing through the point (2,10)

We know that through one point infinite number of lines passing. So through this point infinite number of lines can be pass of such type.

6. If the point (3,2) lies on the graph of the equation 4 y = a x + 6 . Find the value of a .

Solution.

4 y = a x + 6 is the Linear equation   ….(1)

Point (3,2) lies on equation (1)

Putting the value of x = 3 and y = 2 in equation (1)

4 y = a x + 6

4 * 2 = a * 3 + 6

3 a = 8 – 6

3 a = 2

a = 2/3

7. If the point (3,2) lies on the graph of the equation 2 y = a x + 3 . Find the value of a .

Solution.

2 y = a x + 3 is the Linear equation   ….(1)

Point (3,2) lies on equation (1)

Putting the value of x = 3 and y = 2 in equation (1)

2 y = a x + 3

2 * 2 = a * 3 + 3

3 a = 4 – 3

3 a = 1

a = 1/3

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Milan Tomic

Hi. I’m Designer of Blog Magic. I’m CEO/Founder of ThemeXpose. I’m Creative Art Director, Web Designer, UI/UX Designer, Interaction Designer, Industrial Designer, Web Developer, Business Enthusiast, StartUp Enthusiast, Speaker, Writer and Photographer. Inspired to make things looks better.

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